Chequerboard octets are described by their colours, as in HATMAN’s diagram. Non-consecutive (NC) horizontally and vertically in cage pattern. Cages are Ordered (increasing), Non-consecutive, Digitised (last digit of cage total must be same as one of the cell values).
All cages must end with 6,7 or 8; cannot end with 5 because {135} doesn’t meet the Digitised condition.
Valid permutations ending in 6 are [146], [246]
Valid permutations ending in 7 are [137], [357]
Valid permutations ending in 8 are [248], [258], [268], [468]
-> first cells of cages must be {1234}, second cells {3456} and third cells {678}
1. Naked triple {678} in R1C8 + R2C7 + R7C2, locked for D/
1a. R6C3 = {345} -> no 4 in R6C24 + R7C3 (NC)
2. R1C8 + R2C7 = {678} -> no 6,7,8 in R1C7 + R2C8 (NC)
2a. No 6 in R1C7 -> cage at R1C6 cannot be {468}, no 4 in R1C6
2b. R1C6 = {123} -> no 2 in R1C5 (NC)
2c. R2C7 = {678} -> no 7 in R3C7 (NC)
3. R35C3 = {678} -> no 6 in R4C3 (NC)
3a. No 6 in R4C3 -> cage at R4C2 cannot be {468}, no 4 in R4C2
3b. R4C2 = {123} -> no 2 in R35C2 + R4C1 (NC)
3c. R4C3 = {345} -> no 4 in R4C4 (NC)
4. No 4 in R4C4 -> cage at R4C3 cannot be [146/246/248], no 6 in R5C5
5. R35C3 + R5C5 “see” each other so form naked triple {678}, 6 locked for C3
5a. 6 in R35C3 -> one of the cages at R1C1 and R4C2 must be [146/246] (locking cages) -> 4 in R2C2 + R4C3, locked for pink octet, no 4 in R1C12 + R2C1 + R3C4
6. R3C3 = {678} -> no 7 in R2C3 + R3C2 (NC)
6a. R5C3 = {678} -> no 7 in R5C2 (NC)
6b. R5C5 = {78} -> no 7,8 in R5C6 + R6C5 (NC)
6c. R7C2 = {678} -> no 7 in R6C2 + R7C13 + R8C2 (NC)
7. 7 in pink octet only in R1C2 + R2C1 + R3C3 -> no 6 in R2C2 (NC, using cage at R1C1)
7a. R1C1 = {123} -> no 2 in R1C2 + R2C1 (NC)
7b. R2C2 = {345} -> no 4 in R2C3 + R3C2 (NC)
8. Consider placements for 4 in pink octet
R2C2 = 4 => cage at R4C2 not [146/246], no 6 => R3C3 = 6 (hidden single in C3), R4C3 = 3 (not 5, NC) => R4C4 = 5 => cage at R3C4 = [258] (only remaining combination)
or R4C3 = 4 => R4C4 = 6 (not 3,5, NC) => cage at R3C4 = [268] (only remaining combination)
-> R3C4 = 2, placed for pink octet, no 2 in R1C1, R5C5 = 8, placed for D\ and white octet, no 8 in R7C8 + R8C7, R4C4 = {56}
8a. Naked pair {67} in R35C3, locked for C3
8b. R3C4 = 2 -> no 1,3 in R2C4 + R3C5 (NC)
8c. R4C4 = {56} -> no 5 in R4C35 (NC)
8d. R4C3 = {34} -> no 3 in R4C2 (NC)
8e. R4C2 = {12} -> no 1 in R35C2 + R4C1 (NC)
9. R35C3 = {67} -> one of the cages at R1C1 and R4C2 must contain 7 = [137/357] (locking cages) -> 3 in R1C1 + R2C2 + R4C3, locked for pink octet, no 3 in R1C2 + R2C1
10. Cage at R5C4 = [146/137/357], no 4 in R5C4, no 8 in R7C2
10a. 8 on D/ only in R1C8 + R2C7, locked for green octet, no 8 in R4C6
10b. Naked pair {67} in R5C3 + R7C2, locked for grey octet, no 6,7 in R6C4 + R7C1 + R8C2
10c. Naked pair {67} in R5C3 + R7C2, CPE no 6 in R5C2
10d. R7C2 = {67} -> no 6 in R6C2 (NC)
11. R5C3 + R7C2 = {67} -> one of the cages at R4C2 and R5C4 must contain 4 (locking cages), 4 in R46C3, locked for C3
11a. 4 in R46C3, CPE no 4 in R4C5 using D/
12. 8 in pink and green octets only in R1C2 + R2C1 and R1C8 + R2C7, X-Wing no other 8 in R12
12a. 8 in C3 only in R78C3, locked for blue octet, no 8 in R6C12 + R78C4
12b. R6C4 = 8 (hidden single in C4), placed for grey octet, no 8 in R7C1 + R8C2
12c. R6C4 = 8 -> no 7 in R7C4 (NC)
13. R137C2 = {678} (hidden triple in C2)
13a. R3C3 = {67} -> R3C2 = 8 (NC) -> R3C3 = 6 (NC), R4C4 = 5, both placed for D\, R4C3 = 3 (NC), placed for pink octet, R4C2 = 1 (NC), placed for orange octet, R1C1 = 1, R2C2 = 4, both placed for D\, R1C2 = 7, R2C1 = 8 (hidden pair in pink octet), R5C3 = 7
13b. R4C5 = 2, placed for D/ and green octet, no 2 in R2C8
13c. R2C1 = 8 -> no 7 in R3C1 (NC)
[Cracked. The rest is fairly straightforward.]
14. R7C2 = 6 -> cage at R5C4 = [146], all placed for D/ and grey octet, no 4 in R7C1
14a. R6C3 = 4 -> no 3,5 in R6C2 (NC) -> R6C2 = 2, placed for blue octet, no 2 in R5C1 + R78C3
14b. R6C2 = 2 -> no 3 in R5C2 + R6C1 (NC) -> R5C2 = 5, placed for blue octet, no 5 in R6C1 + R78C3
14c. R5C2 = 5 -> R5C1 = 3 (NC), placed for blue octet, no 3 in R78C4 -> R7C4 = 4
14d. R8C12 = [53], R4C1 = 4, R7C1 = 2
15. R2C7 = 7, placed for green octet -> R3C56 = [53], placed for green octet -> R1C7 = 4, placed for green octet -> R4C6 = 6, R4C178 = [784]
16. R6C6 = 7 -> no 6 in R6C57, no 8 in R7C6 (NC)
and the rest is naked singles, without using octets, diagonals and NC.